Many exhaust purification systems have been proposed in order to allow nitrogen oxide (NOx) contained in exhaust gas to be purified. For example, an exhaust purification system Patent Document 1 comprises a burner system configured to increase the temperature of exhaust gas, a filter configured to collect particulate matter (PM) contained in the exhaust gas, an NOx adsorption material configured to temporarily adsorb nitrogen oxide contained in the exhaust gas, and a combustion device configured to combust the nitrogen oxide desorbed from the NOx adsorption material; the burner system, the filter, the NOx adsorption material, and the combustion device are all provided in an exhaust passage. In this exhaust purification apparatus, a filter with PM accumulated therein is recovered by using the burner system to increase the temperature of the filter to combust and remove the PM. At this time, the temperature of the NOx adsorption material also increases. Thus, the NOx adsorbed on the NOx adsorption material is desorbed. The desorbed NOx is reduced and removed by the combustion device.    Patent Document 1: Japanese Patent Laid-Open No. 2005-207281